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Full text of "Men Of Mathematics"

MEN OF MATHEMATICS
geometry, Clifford was no servile copyist but a man with a
brilliantly original mind of Ms own, of whom it may be saids as
Newton said of Cotes, 4Jf he had lived we might have known
something.' The reader who is acquainted with any of the better
available popular accounts of reiativistic physics and the wave
theory of electrons will recognize several curious adumbrations
of current theories in Clifford's brief prophecy.
'Kiemann has shown that as there are different Mnds of lines
and surfaces, so there are different kinds of space of three
dimensions; and that we can only find out by experience to
which of these kinds the space hi which we live belongs. In
particular, the axioms of plane geometry are true within the
limits of experiment on the surface of a sheet of paper, and yet
we know that the sheet is really covered with a number of small
ridges and furrows, upon which (the total curvature being not
zero) these axioms are not true. Similarly, he says, although the
axioms of solid geometry are true within the limits of experi-
ment for finite portions of our space, yet we have no reason to
conclude that they are true for very small portions; and if any
help can be got thereby for the explanation of physical pheno-
mena, we may have reason to conclude that they are not true
for very small portions of space.
*I wish here to indicate a manner in which these speculations
may be applied to the investigation of physical phenomena. I
hold in fact
(1)  That small portions of space are in fact of a nature analo-
gous to little hills on a surface which is on the average flat;
namely, that the ordinary laws of geometry are not valid in
them.
(2)  That this property of being curved or distorted is con-
tinually being passed on from one portion of space to another
after the manner of a wave.
(3)  That this variation of the curvature of space is what
really happens in that phenomenon which we call the motion of
matter, whether ponderable or ethereal.
(4)  That in the physical world nothing else takes place but
tbis variation, subject (possibly) to the law of continuity.
*I am endeavouring in a general way to explain the laws of
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